Find the interval/s in which the function $f: \mathbb{R} \to \mathbb{R}$ defined by $f(x) = xe^x$, is increasing.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $[-1, \infty)$ ##
We have, $f(x) = xe^x$
$\Rightarrow f'(x) = e^x(x + 1)$
For $f(x)$ to be increasing, we have $f'(x) = e^x(x + 1) \geq 0$
$\Rightarrow x \geq -1$ as $e^x > 0, \forall x \in \mathbb{R}$
Hence, the required interval where $f(x)$ increases is $[-1, \infty)$.